188 citations · 367 across the 31 of their papers we have counts for
12 papers · 1 filter
Riemannian Laplace approximations for Bayesian neural networks
Federico Bergamin, Pablo Moreno-Muñoz, Søren Hauberg +1
Bayesian neural networks often approximate the weight-posterior with a Gaussian distribution. However, practical posteriors are often, even locally, highly non-Gaussian, and empiri…
Model-agnostic out-of-distribution detection using combined statistical tests
Federico Bergamin, Pierre-Alexandre Mattei, Jakob D. Havtorn +5
We present simple methods for out-of-distribution detection using a trained generative model. These techniques, based on classical statistical tests, are model-agnostic in the sens…
Reparametrization Invariance in non-parametric Causal Discovery
Martin Jørgensen, Søren Hauberg
Causal discovery estimates the underlying physical process that generates the observed data: does X cause Y or does Y cause X? Current methodologies use structural conditions to tu…
Geometrically Enriched Latent Spaces
Georgios Arvanitidis, Søren Hauberg, Bernhard Schölkopf
A common assumption in generative models is that the generator immerses the latent space into a Euclidean ambient space. Instead, we consider the ambient space to be a Riemannian m…
Isometric Gaussian Process Latent Variable Model for Dissimilarity Data
Martin Jørgensen, Søren Hauberg
We present a probabilistic model where the latent variable respects both the distances and the topology of the modeled data. The model leverages the Riemannian geometry of the gene…
Fast and Robust Shortest Paths on Manifolds Learned from Data
Georgios Arvanitidis, Søren Hauberg, Philipp Hennig +1
We propose a fast, simple and robust algorithm for computing shortest paths and distances on Riemannian manifolds learned from data. This amounts to solving a system of ordinary di…
Only Bayes should learn a manifold (on the estimation of differential geometric structure from data)
Søren Hauberg
We investigate learning of the differential geometric structure of a data manifold embedded in a high-dimensional Euclidean space. We first analyze kernel-based algorithms and show…
Probabilistic Riemannian submanifold learning with wrapped Gaussian process latent variable models
Anton Mallasto, Søren Hauberg, Aasa Feragen
Latent variable models (LVMs) learn probabilistic models of data manifolds lying in an \emph{ambient} Euclidean space. In a number of applications, a priori known spatial constrain…
Latent Space Oddity: on the Curvature of Deep Generative Models
Georgios Arvanitidis, Lars Kai Hansen, Søren Hauberg
Deep generative models provide a systematic way to learn nonlinear data distributions, through a set of latent variables and a nonlinear "generator" function that maps latent point…
A Locally Adaptive Normal Distribution
Georgios Arvanitidis, Lars Kai Hansen, Søren Hauberg
The multivariate normal density is a monotonic function of the distance to the mean, and its ellipsoidal shape is due to the underlying Euclidean metric. We suggest to replace this…
Metrics for Probabilistic Geometries
Alessandra Tosi, Søren Hauberg, Alfredo Vellido +1
We investigate the geometrical structure of probabilistic generative dimensionality reduction models using the tools of Riemannian geometry. We explicitly define a distribution ove…
Probabilistic Solutions to Differential Equations and their Application to Riemannian Statistics
Philipp Hennig, Søren Hauberg
We study a probabilistic numerical method for the solution of both boundary and initial value problems that returns a joint Gaussian process posterior over the solution. Such metho…